Stability of ternary antiderivation in ternary Banach algebras via fixed point theorem

In this paper, we introduce the concept of ternary antiderivation on Banach algebras and investigate stability in algebras, associated to $(\alpha,\beta)$-functional inequality: \begin{align*} &\Vert \mathcal{F}(x+y+z)-\mathcal{F}(x+z)-\mathcal{F}(y-x+z)-\mathcal{F}(x-z)\Vert \nonumber\\ &\leq \Vert \alpha (\mathcal{F}(x+y-z)+\mathcal{F}(x-z)-\mathcal{F}(y))\Vert + \beta (\mathcal{F}(x-z)\\ &+\mathcal{F}(x)-\mathcal{F}(z))\Vert \end{align*} where $\alpha$ $\beta$ are fixed nonzero complex numbers with $\vert\alpha \vert +\vert \vert<2$ by using point method.